In a known device of this type, disclosed in German published patent application DE 43 41 934 A1, provision is made to calculate the filling time for the fluid, if need be, by taking into account the temperature detected by a temperature sensor disposed in the distributor. However, it has been learned by experience with devices of this type that the measurement of the fluid temperature, and the adaptation of the filling time by means of software programs that take the fluid temperature into account, does not produce satisfactory results with regard to filling precision. This drawback is particularly the case with products that have a very temperature-dependent flow behavior.